Examples of Chaotic Dynamics
Chaos on the Real Number Line
Functions dealing with the real number line are probably what you are most familiar with. These functions take R1 R1, meaning that the real number line (R1) is being mapped to the real number line. (See Function Basics - Algebra)
A good example of one of these functions is the quadratic family.
- The Quadratic Family - A group of typical R1 R1 functions, analyzed for bifurcations.
- The Cantor Set - A group of points on the real number line that have interesting properties.
Chaos in the Plane
Chaos on the Complex Plane
- The Mandelbrot Set - A group of complex numbers that do not diverge under certain conditions.
- The Julia Sets - Sets of complex numbers that do not escape to infinity under iteration.